A commognitive lens on the transition from naive empiricism to the generic example: the case of figural patterns
The purpose of this article is to deepen our understanding of the transition from substantiating a formula for a figural pattern by naive empiricism to substantiation by a generic example. We conceptualise this transition using the commognitive constructs meta-rules, commognitive conflict, and reification. Our conceptualisation is exemplified by a description of the learning process of a group of four pre-service mathematics teachers (PSTs) engaged in justifying formulas for figural patterns. The PSTs initially substantiated the formula for a figural pattern by naive empiricism. After watching video-based suggested solutions, in which the structure of the figural pattern was made explicit by grouping the dots in the figural pattern, a commognitive conflict emerged. We show how this conflict was resolved in the next session, after the teacher initiated a plenary discussion on how a formula for a figural pattern should be substantiated. We demonstrate how the PSTs’ discourse developed during this process.
Publisert i Research in Mathematics Education, 2026
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